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Known as input in the Numerical Weather Prediction (NWP) models, Microwave Radiation Imager (MWRI) data have been widely distributed to the user community. With the development of remote sensing technology, improving the geolocation accuracy of MWRI data are required and the first step is to estimate the geolocation error accurately. However, the traditional method, such as the coastline inflection method (CIM), usually has the disadvantages of low accuracy and poor anti-noise ability. To overcome these limitations, this paper proposes a novel <inline-formula> <math display="inline"> <semantics> <msub> <mi>ℓ</mi> <mi>p</mi> </msub> </semantics> </math> </inline-formula> iterative closest point coastline inflection method (<inline-formula> <math display="inline"> <semantics> <msub> <mi>ℓ</mi> <mi>p</mi> </msub> </semantics> </math> </inline-formula>-ICP CIM). It assumes that the field of views (FOVs) across the coastline can degenerate into a step function and employs an <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>ℓ</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>&#8804;</mo> <mi>p</mi> <mo>&lt;</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> sparse regularization optimization model to solve the coastline point. After estimating the coastline points, the ICP algorithm is employed to estimate the corresponding relationship between the estimated coastline points and the real coastline. Finally, the geolocation error can be defined as the distance between the estimated coastline point and the corresponding point on the true coastline. Experimental results on simulated and real data sets show the effectiveness of our method over CIM. The accuracy of the geolocation error estimated by <inline-formula> <math display="inline"> <semantics> <msub> <mi>ℓ</mi> <mi>p</mi> </msub> </semantics> </math> </inline-formula>-ICP CIM is up to <inline-formula> <math display="inline"> <semantics> <mrow> <mn>0.1</mn> </mrow> </semantics> </math> </inline-formula> pixel, in more than <inline-formula> <math display="inline"> <semantics> <mrow> <mn>90</mn> <mo>%</mo> </mrow> </semantics> </math> </inline-formula> of cases. We also show that the distribution of brightness temperature near the coastline is more consistent with the real coastline and the average geolocation error is reduced by <inline-formula> <math display="inline"> <semantics> <mrow> <mn>63</mn> <mo>%</mo> </mrow> </semantics> </math> </inline-formula> after geolocation error correction.